Solve 768v^6y^7/36v^2y^3

$$\frac { 768 v ^ { 6 } y ^ { 7 } } { 36 v ^ { 2 } y ^ { 3 } }$$

Evaluate

$$\frac{64\left(vy\right)^{4}}{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{768^{1}v^{6}y^{7}}{36^{1}v^{2}y^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{768^{1}}{36^{1}}v^{6-2}y^{7-3}$$

Subtract 2 from 6.

$$\frac{768^{1}}{36^{1}}v^{4}y^{7-3}$$

Subtract 3 from 7.

$$\frac{768^{1}}{36^{1}}v^{4}y^{4}$$

Reduce the fraction \frac{768}{36} to lowest terms by extracting and canceling out 12.

$$\frac{64}{3}v^{4}y^{4}$$

Differentiate w.r.t. y

$$\frac{256y^{3}v^{4}}{3}$$